An almost third order finite difference scheme for singularly perturbed reaction-diffusion systems |
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Authors: | C. Clavero J.L. Gracia |
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Affiliation: | Department of Applied Mathematics, University of Zaragoza, Spain |
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Abstract: | This paper addresses the numerical approximation of solutions to coupled systems of singularly perturbed reaction-diffusion problems. In particular a hybrid finite difference scheme of HODIE type is constructed on a piecewise uniform Shishkin mesh. It is proved that the numerical scheme satisfies a discrete maximum principle and also that it is third order (except for a logarithmic factor) uniformly convergent, even for the case in which the diffusion parameter associated with each equation of the system has a different order of magnitude. Numerical examples supporting the theory are given. |
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Keywords: | Reaction-diffusion systems High order Uniform convergence Shishkin mesh Hybrid HODIE methods |
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